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February 9th, 2019, 09:39 AM   #11
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How do you intend to do operations with these numbers? Having $x > 1$ and $x < 1$ raises the prospect of having many undefined results, because the two relations give conflicting results. The definitions are immensely vague as well. We don't have any idea of the scale of $x$. Is it "close" to $1$ or is it very large or very small? These things all have a dramatic effect on the qualities of the results of operations involving $x$.

Perhaps most importantly, what do you intend to achieve? New numbers that extend different systems work best when they have a specific property that fills a specific need. Thus $i$ is a square root of $-1$: all other properties are derived from this. Infinitesimals are defined to be positive and smaller than all positive reals for a specific purpose which we can then use to discover other of their properties.

Last edited by skipjack; February 9th, 2019 at 02:09 PM.
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February 9th, 2019, 10:06 AM   #12
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Originally Posted by Extrazlove View Post
My definition is simple X is greater and less than 1 without being equal to 1.
So X do not belong to R,
and since I used <and> to define it, it does not belong to C either.
You haven't defined anything at all. The expression $x < y$ has a meaning in the real numbers. If suddenly you claim that $y$ isn't a real number, then you have to define what $x < y$ even means. Here is an example:

Suppose I tell you that $x < $ 1997 Honda Accord. What does that mean? So far the answer is "nothing" since $<$ has meaning for real numbers, not cars. It would be my responsibility to explain what that means if I want to use it in some context.

It also seems you believe that $<$ is meaningful on $\mathbb{C}$ so I should point out this is not true. The complex numbers are not a totally ordered field.

Last edited by skipjack; February 9th, 2019 at 02:12 PM.
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February 9th, 2019, 10:11 AM   #13
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Quote:
Originally Posted by Extrazlove View Post
My definition is simple X is greater and less than 1 without being equal to 1.
So X do not belong to R,
and since I used <and> to define it, it does not belong to C either.
Are you a student attending math classes?

Last edited by skipjack; February 9th, 2019 at 02:12 PM.
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February 9th, 2019, 11:33 AM   #14
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Quote:
Originally Posted by v8archie View Post
How do you intend to do operations with these numbers? Having $x > 1$ and $x < 1$ raises the prospect of having many undefined results, because the two relations give conflicting results. The definitions are immensely vague as well. We don't have any idea of the scale of $x$. Is it "close" to $1$ or is it very large or very small. These things all have a dramatic effect on the qualities of the results of operations involving $x$.

Perhaps most importantly, what do you intend to achieve? New numbers that extend different systems work best when they have a specific property that fills a specific need. Thus $i$ is a square root of $-1$: all other properties are derived from this. Infinitesimals are defined to be positive and smaller than all positive reals for a specific purpose which we can then use to discover other of their properties.
If, for example, I say that X < 1 and X > 1
if X is a real number, then X would be equal 1 and there is no contradiction.

It is the fact to say that X is different from 1 which means that X is not real.

And since I used the <and> to set it, X would not be a complex number.

Last edited by skipjack; February 9th, 2019 at 02:14 PM.
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February 9th, 2019, 11:38 AM   #15
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Quote:
Originally Posted by Extrazlove View Post
If, for example, I say that X < 1 and X > 1
if X is a real number, then X would be equal 1 and there is no contradiction.

It is the fact to say that X is different from 1 which means that X is not real.

And since I used the <and> to set it, X would not be a complex number.
And the point of all this is?

Last edited by skipjack; February 9th, 2019 at 02:14 PM.
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February 9th, 2019, 11:40 AM   #16
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Originally Posted by Denis View Post
Are you a student attending math classes?
No. I have a bac +5 in automatic; I'm looking for work.
I have always found the strange Dirac impulse and I want to construct such a strange number group.

Last edited by skipjack; February 9th, 2019 at 02:17 PM.
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February 9th, 2019, 12:00 PM   #17
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And the point of all this is?
have a prize for discovering the numbers and let the mathematicians find what can serve its numbers.
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February 9th, 2019, 12:34 PM   #18
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have a prize for discovering the numbers and let the mathematicians find what can serve its numbers.
Anyone with a certain amount of wit can come up with a new number system. There are a lot of them out there. But the effort of proving that they can be useful is on you. No recognition will come unless you find a use for them.

-Dan
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February 9th, 2019, 01:14 PM   #19
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Sorry. I can do that, but I do not have the means to do it.
I do not even have a computer or a smartphone; I sometimes use my father's smartphone.
That's why I'm here so you can do that.
I can say that all of its numbers have the same cardinal as the set R.

Last edited by skipjack; February 9th, 2019 at 02:19 PM.
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February 9th, 2019, 02:25 PM   #20
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Why can you say that?
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